Equilibrium Specification and Structure of Technology: a Factor Substitution Analysis in French Industrial Demand of Energy

In this paper we attempt to provide evidence on the structure of technology in the three industrial branches of French economy, when capital is treated as quasi-fixed input. However instead of choosing a single functional form as an approximation to the variable cost function, modified versions of three commonly used flexible functional forms are estimated: (i) the Translog, (ii) the Generalized Leontief and (iii) the Symmetric Generalized McFadden. While maintaining the same data set and the same assumptions about technology, an empirical comparison of alternative flexible models is attempted. A theoretical framework is developed which allows for derivation and estimation of long run elasticities, capacity utilization and their derivatives in situations where full static equilibrium is not a tenable assumption. This original method holds for either single or multiple fixed input models. A specification test is proposed and conducted to assess the adequacy of the full equilibrium model and find that the long run equilibrium hypothesis is rejected for all three branches. The derivatives of long run elasticities with respect to energy price give insight on the evolution of technological parameters in response to fluctuations of energy prices. The issues analyzed in this paper are not merely of theoretical interest, but are also of practical concern.